Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}8x-2y &= -1 \\ -3x+y &= 4\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {3x+4}$ Substitute this expression for $y$ in the first equation. $8x-2({3x + 4}) = -1$ $8x - 6x - 8 = -1$ Simplify by combining terms, then solve for $x$ $2x - 8 = -1$ $2x = 7$ $x = \dfrac{7}{2}$ Substitute $\dfrac{7}{2}$ for $x$ back into the top equation. $8( \dfrac{7}{2})-2y = -1$ $28-2y = -1$ $-2y = -29$ $y = \dfrac{29}{2}$ The solution is $\enspace x = \dfrac{7}{2}, \enspace y = \dfrac{29}{2}$.